This past Sat, Ask This Old House had a segment on robot lawn mowers. Unfortunately, they don't seem to have this on their web archive yet, but from memory:
They had two units. Both were battery operated completely electric, and looked to run off 12v. The smaller one had a single blade (I think it was12"), the large had three small blades (that actually looked like food processor blades). The blades are sunk into the body for safety to avoid cutting feet.
The smaller unit was actually more expensive because it would home in on it's charger and recharge itself when needed, the larger one needed to be manually recharged. Both used a random pattern, with a buried wire to keep it in bounds.
What was interesting was that larger unit was less than $500. I would think that, for the safety reasons, anyone looking to work on methods for a robot mower would be better of starting with one of these as the base.
Now, hopefully they add this to the site soon, as I don't recall the companies at all.